It's going to be a few years before your toddler's LiveJournaling, but for now you can share the latest baby news and developments with webapp TotSpot. TotSpot incorporates features of many popular social media sites to create a virtual baby book for parents to catalog their child's growth. With TotSpot you can upload photos and video, and keep a journal about your child that tracks new firsts (first words, first steps, first time not terrified by the animatronic stegosaurus at the local water park, etc.) and new favourite things. You can input data on growth and development to create a virtual growth chart. Totspot even has a Twitter-esque micro blogging feature for quick and easy updates about what you and the baby are doing.
Parents concerned about privacy can restrict who sees what on TotSpot. Set your child's TotSpot page to be completely private so it's essentially an online baby book for your personal use, share it with friends and family via invitation, or open it to other TotSpot members for baby bragging rights. There is currently no privacy setting to completely open the profile up to the greater web.